The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics...

The Mindset Revolution:Teaching mathematics for a growth mindset

Jo BoalerProfessor of Mathematics EducationStanford University

Carol Dweck, 2006, Mindset: The New Psychology of Success

The myth of mathematics Being good at math is a “gift” –

some people are naturally good at math, some are not

Shake It Up Chicago

Hollywood

Hollywood

Hollywood

Brain Plasticity

When learning happens …

A synapse fires

Synapses are like footprints in the sand – the brain follows the footprints and makes them deeper the more they are followed

Plasticity

Learning creates and strengthens synapses

The plasticity of the brain means that these connections grow into adult-hood

If Pathways aren’t followed they may be discarded

“use it or lose it”

Brain growth

London ‘Black Cab’ Drivers

“The Knowledge” – 25,000 streets and 20,000 landmarks

Brain Growth

London taxi drivers have a larger hippocampus than London bus drivers

A 6-year old girl

Had half of her brain removed Amazed doctors and scientists -

within months she had recovered functions from the “missing” side of the brain

Neuroplasticity refers to the life long capacity of the brain to change and rewire itself in response to learning and experience.

We know taking advanced math classes is the best predictor for success in college. Nothing would make us happier than being able to produce only graduates that have calculus on their transcripts! However, brain theory supports the reality that confounding student situations interfere with their ability to focus and succeed as they move through advanced mathematics in high school.

We live in an affluent community. Most of our students are fortunate to come from families where education matters and parents have the means to support and guide their children in tandem with us their teachers. Not all of them. We are concerned about the others who for reasons that are often objective (poor math background, lack of support at home, low retention rate, lack of maturity etc) cannot pass our Algebra II regular lane course.

Many of them are VTP students or under-represented minorities. Others are serious, committed special ed students (etc)

From a local, public high school math dept in 2012

Brain research tells us: Every child can excel in

mathematics in school, from elementary to high school

Ability?

Each new learning experiences changes your “ability”.

We use fixed ability language all the time – high and low kids etc

Laurent Schwartz ‘A Mathematician Grappling with his Century’

..I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent.  And it is true that I was, and still am, rather slow.  I need time to seize things because I always need to understand them fully.  Even when I was the first to answer the teacher's questions, I knew it was because they happened to be questions to which I already knew the answer.  But if a new question arose, usually students who weren't as good as I was answered before me. Towards the end of the eleventh grade, I secretly thought of myself as stupid.  I worried about this for a long time.    I never talked about this to anyone, but I always felt convinced that my imposture would someday be revealed: the whole world and myself would finally see that what looked like intelligence was really just an illusion.  If this ever happened, apparently no one noticed it, and I’m still just as slow. (...)At the end of the eleventh grade, I took the measure of the situation, and came to the conclusion that rapidity doesn't have a precise relation to intelligence.  What is important is to deeply understand things and their relations to each other.  This is where intelligence lies.  The fact of being quick or slow isn't really relevant.  Naturally, it's helpful to be quick, like it is to have a good memory.  But it's neither necessary nor sufficient for intellectual success.

How important are the ideas that students hold about ability?

Carol Dweck: Mindset

Mindset: The New Psychology of Success. (2007) Fixed - math ability is a “gift” Growth – math ability or

“smartness” grows with experienceGrowth mindset behaviors – persistence, learn from mistakes, determination to keep going, encouraged by other’s successAffects students from across the achievement spectrum Role of parents in encouraging fixed

mindset

7th grade students with a growth mindset outperform those with a fixed mindset in math

The impact of a mindset intervention (same math teacher, same curriculum)

Research on Mindset and equity African American students show

sharpest increase in grades and valuing school

A growth mindset eliminates any gender gaps eg in highest SAT levels

Mindset and gender

High achieving 5th grade girls did not cope well with challenge

The higher their IQ the more difficulty they had, in boys the reverse was true

At the end of 8th grade there was a gender gap but only among fixed mindset students

Mindset and gender

Calculus at Columbia Stereotyping is alive and well Stereotyping only affected those

with a fixed mindset, their confidence eroded over the semester and they abandoned plans to pursue STEM subjects

Implications

Seeing math as a gift not only makes students vulnerable to lack of confidence but vulnerable to stereotypes too

Having a growth mindset is what we want all teachers and all students to have

The big message

Intelligence is malleable, but … Students, teachers, schools,

parents treat math learners as though it is relatively fixed

Brainstorm with others around you - which aspects of schools / math teaching encourage a FIXED mindset? Choose your top 3

MessagesMindset

+ Math

Messages

Messages

Messagesmistakes

grading

&

feedback

grouping

tasksquestions asked

norm se

tting

What has mindset got to do with my math teaching?

Today - mindset

Grouping Classroom Math Tasks Assessment & Grading Mistakes Messages

Ability Grouping

Burris, C., Heubert, J., & Levin, H. (2006).

Accelerating Mathematics Achievement Using Heterogeneous Grouping.

American Educational Research Journal, 43(1), 103-134.

Ability Grouping

In England researchers followed 14000 children through years 4 and 6 comparing those taught in sets with those grouped heterogeneously over the period of a year.

Nunes, Bryant, Sylva & Barros, 2009

Classroom Math Tasks

How do you maintain a growth mindset when math class is a series of closed questions that you get right or wrong?

Most math classrooms offer math as a performance subject not a learning subject.Rachel Lambert’s 6 year old son:

“Math is too much answer time and not enough learning time”

Tasks need to give students the space to learn.

Growth Mindset Task Framework

Task focuses on learning: opportunities to learn something rather than demonstrate what you know

Openness- Ways of seeing- Multiple entry points- Multiple paths / strategies Clear learning goals and opportunities for feedback.

An example

Comes from a 5 week algebra class I taught with graduate students in summer school

Our goal: to teach algebra as a problem solving tool

Underachieving 7th, 8th grade students

Tasks – Ruth Parker, Mark Driscoll, SMILE, Points of Departure

How many blocks are in case 100? \

Sarah Kate Selling

Luke Jorge Carlos

Case n has (n+1)2 blocks

Recursive pattern: +5, +7…

Jorge

Carlos

Luke

Case 1 Case 2 Case 3

Recognizing different ways of seeing

Explaining different ways of seeing

Resolving through connecting

A case: mathematical practices & heterogeneity Gauss

What engages the students so strongly and for so long? And what does it have to do with growth mindset teaching?

3 boys video

When math tasks are opened for Different ways of seeing Different methods / pathways Different representations

The opportunities for learning and developing a growth mindset are increased

1 ÷ 2/3

Cathy Humphreys, 7th graders Connecting Mathematical Ideas – video cases Mathematics as sense-making which encourages:

Different ways of seeing Different methods / pathways Different representations

Assessment &Grading

Grades Diagnostic

Feedback

Diagnostic Feedback significantly higher

Grades Diagnostic

Feedback Diagnostic

Feedback& Grades

Diagnostic Feedback significantly higher

(Butler)

Timed Tests?

From 1st to 5th grade

A Timed Test of 50 questions to finish in 3 minutes

From neuroscience ..

Math should never be associated with speed

From Sian Beilock:

no relation between stress and prior achievement

Math stress cuts across the achievement spectrum –particularly affecting girls

From Sian Beilock:

4th grade:

2nd grade:

www.joboaler.com

“Every time a student makes a mistake in math they grow a new synapse” (Carol Dweck)

Mistakes

Every mistake grows a synapse

Mistakes are good They are the time your brain is

growing Students should be making

mistakes Students hate making mistakes –

because they have been brought up in a performance and not a learning culture

Students & most teachers view them negatively

Reposition mistakes

In classroom norms In 1:1 interactions

Messages

www.brainology.com (Geoff Cohen) “I am giving you this feedback

because I believe in you” Resulted in significant

achievement gains, again especially for minority students.

My freshmen

What is the big messages or message(s) that the students took away?

Stanford freshmen

To conclude It is critically important that

teachers and students are encouraged to develop a ‘growth mindset’

The ideas I have shared for teaching and assessing are not new but the reason for implementing them – to develop growth mindsets - is an important impetus for change, and an idea that many teachers and schools understand

The ways teachers teach math has huge implications for students’ mindsets

Udacity & Stanford ‘MOOC’

Teaching Mathematics for the Common Core

https://www.udacity.com

Talk no longer than 90 seconds before engaging the learner